{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c5bbe4ed-8913-475f-a386-54dad79f1bf6",
   "metadata": {},
   "source": [
    "# Binomial Trees and Trinomial Trees"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69d0cd6a-0840-457e-8635-456e2a4837ae",
   "metadata": {},
   "source": [
    "# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bf24a14-5e4c-49cf-81c4-7d66efa1ea59",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Load the Libs we need"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7bed8bce-60fb-4a06-b2c7-70a4f83ee7a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import Lib\n",
    "import pandas as pd\n",
    "import datetime as dt\n",
    "import pytz\n",
    "import os\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import yfinance as yf\n",
    "import numpy as np\n",
    "import scipy.stats as si\n",
    "import math\n",
    "import networkx as nx\n",
    "\n",
    "# import module\n",
    "from datetime import datetime, timezone\n",
    "from datetime import date, time\n",
    "from math import trunc\n",
    "from dateutil.parser import parse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eed61505-7cf1-4fd9-8fd1-1678375ef267",
   "metadata": {},
   "source": [
    "## Binomial Tree Model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dba6e58e-dde4-4d31-bacf-8c9f98c63b96",
   "metadata": {},
   "source": [
    "#### European Options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1f96c186-066d-481d-9bf4-641e5e71ef4e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n = 2\n",
      "European call\n",
      "8.081246948239023\n",
      "European put\n",
      "7.960336520813991\n",
      "~~~~~~~~~~~~~~~~~~~~\n",
      "n = 10\n",
      "European call\n",
      "8.176296974444437\n",
      "European put\n",
      "8.055386547019513\n",
      "~~~~~~~~~~~~~~~~~~~~\n",
      "n = 100\n",
      "European call\n",
      "8.026229025058432\n",
      "European put\n",
      "7.90531859763425\n"
     ]
    }
   ],
   "source": [
    "def mb_binomial_tree_european(n, S, K, T, r, v, otype='call'):\n",
    "    dt = T/n\n",
    "    u = math.exp(v * math.sqrt(dt))\n",
    "    d = 1/u\n",
    "    p = (math.exp(r*dt) - d)/(u - d)\n",
    "    \n",
    "    # Price tree\n",
    "    price_tree = np.zeros([n+1, n+1])\n",
    "    \n",
    "    for i in range(n+1):\n",
    "        for j in range(i+1):\n",
    "            price_tree[j, i] = S * (u ** (i - j)) * (d ** j)\n",
    "\n",
    "    # Option value\n",
    "    option = np.zeros([n+1, n+1])\n",
    "\n",
    "    # Calculate the option price at expiration\n",
    "    if otype == 'call':\n",
    "        option[:, n] = np.maximum(np.zeros(n+1), (price_tree[:, n]-K))\n",
    "    elif otype == 'put':\n",
    "        option[:, n] = np.maximum(np.zeros(n+1), (K - price_tree[:, n]))\n",
    "    else:\n",
    "        raise ValueError(\"Invalid option type. Please use 'call' or 'put'\")\n",
    "\n",
    "    # Calculate option price at t=0\n",
    "    for i in range(n-1, -1, -1):\n",
    "        for j in range(0, i+1):\n",
    "            option[j, i] = math.exp(-r * dt) * (p * option[j, i + 1] + (1-p) * option[j + 1, i + 1])\n",
    "    \n",
    "    return option[0, 0]\n",
    "\n",
    "print(\"n = 2\")\n",
    "# Testing the function with a European call\n",
    "print(\"European call\")\n",
    "print(mb_binomial_tree_european(2, 100, 105, 1, 0.05, 0.2, 'call'))\n",
    "# Testing the function with a European put\n",
    "print(\"European put\")\n",
    "print(mb_binomial_tree_european(2, 100, 105, 1, 0.05, 0.2, 'put'))\n",
    "print(\"~~~~~~~~~~~~~~~~~~~~\")\n",
    "print(\"n = 10\")\n",
    "# Testing the function with a European call\n",
    "print(\"European call\")\n",
    "print(mb_binomial_tree_european(10, 100, 105, 1, 0.05, 0.2, 'call'))\n",
    "# Testing the function with a European put\n",
    "print(\"European put\")\n",
    "print(mb_binomial_tree_european(10, 100, 105, 1, 0.05, 0.2, 'put'))\n",
    "print(\"~~~~~~~~~~~~~~~~~~~~\")\n",
    "print(\"n = 100\")\n",
    "# Testing the function with a European call\n",
    "print(\"European call\")\n",
    "print(mb_binomial_tree_european(100, 100, 105, 1, 0.05, 0.2, 'call'))\n",
    "# Testing the function with a European put\n",
    "print(\"European put\")\n",
    "print(mb_binomial_tree_european(100, 100, 105, 1, 0.05, 0.2, 'put'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3a712eab-0401-4444-9d6a-62f3049317bf",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "99b2bf0f-79ba-456b-a2fa-86360e07d009",
   "metadata": {},
   "source": [
    "#### Visualizing the underlying prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3c78df01-1c43-4838-acb9-71f1a3d6d56d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def mb_binomial_tree_underlying_prices(n, S, K, T, r, v):\n",
    "    # Delta time\n",
    "    dt = T / n\n",
    "    # Up and down factors\n",
    "    u = math.exp(v * math.sqrt(dt))\n",
    "    d = 1 / u\n",
    "    # Risk-neutral probability\n",
    "    p = (math.exp(r * dt) - d) / (u - d)\n",
    "\n",
    "    # Initialize stock price tree\n",
    "    stock = np.zeros([n + 1, n + 1])\n",
    "    for i in range(n + 1):\n",
    "        for j in range(i + 1):\n",
    "            stock[j, i] = S * (u ** (i - j)) * (d ** j)\n",
    "\n",
    "    # Displaying the binomial tree graph\n",
    "    binomial_tree = nx.Graph()\n",
    "\n",
    "    for i in range(n + 1):\n",
    "        for j in range(i + 1):\n",
    "            binomial_tree.add_node((j, i), pos=(i, -(2 * j - i)), value=stock[j, i])\n",
    "\n",
    "    for i in range(n):\n",
    "        for j in range(i + 1):\n",
    "            binomial_tree.add_edge((j, i), (j, i + 1))\n",
    "            binomial_tree.add_edge((j, i), (j + 1, i + 1))\n",
    "\n",
    "    pos = nx.get_node_attributes(binomial_tree, 'pos')\n",
    "    labels = nx.get_node_attributes(binomial_tree, 'value')\n",
    "    labels = {key: f'{value:.2f}' for key, value in labels.items()}\n",
    "\n",
    "    nx.draw(binomial_tree, pos, labels=labels, with_labels=True, node_color='skyblue', node_size=1500)\n",
    "    plt.show()\n",
    "\n",
    "mb_binomial_tree_underlying_prices(2, 100, 105, 1, 0.05, 0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5fddb966-ae85-4050-b7ce-0805df5050f1",
   "metadata": {},
   "source": [
    "#### Visualizing the call prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b09df40b-4cf2-4306-9a96-1b687de4801d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def mb_binomial_tree_european_call(n, S, K, T, r, v):\n",
    "    # Delta time\n",
    "    dt = T / n\n",
    "    # Up and down factors\n",
    "    u = math.exp(v * math.sqrt(dt))\n",
    "    d = 1 / u\n",
    "    # Risk-neutral probability\n",
    "    p = (math.exp(r * dt) - d) / (u - d)\n",
    "\n",
    "    # Initialize stock price tree\n",
    "    stock = np.zeros([n + 1, n + 1])\n",
    "    for i in range(n + 1):\n",
    "        for j in range(i + 1):\n",
    "            stock[j, i] = S * (u ** (i - j)) * (d ** j)\n",
    "\n",
    "    # Initialize option price tree\n",
    "    option = np.zeros([n + 1, n + 1])\n",
    "    option[:, n] = np.maximum(np.zeros(n + 1), stock[:, n] - K)\n",
    "\n",
    "    # Calculate the option price at t=0\n",
    "    for i in range(n - 1, -1, -1):\n",
    "        for j in range(i + 1):\n",
    "            option[j, i] = math.exp(-r * dt) * (p * option[j, i + 1] + (1 - p) * option[j + 1, i + 1])\n",
    "\n",
    "    # Displaying the binomial tree graph\n",
    "    binomial_tree = nx.Graph()\n",
    "\n",
    "    for i in range(n + 1):\n",
    "        for j in range(i + 1):\n",
    "            binomial_tree.add_node((j, i), pos=(i, 2 * j - i - n), value=option[j, i] if j <= i else None)\n",
    "\n",
    "    for i in range(n):\n",
    "        for j in range(i + 1):\n",
    "            binomial_tree.add_edge((j, i), (j, i + 1))\n",
    "            binomial_tree.add_edge((j, i), (j + 1, i + 1))\n",
    "\n",
    "    pos = nx.get_node_attributes(binomial_tree, 'pos')\n",
    "    labels = nx.get_node_attributes(binomial_tree, 'value')\n",
    "    labels = {key: f'{value:.2f}' for key, value in labels.items() if value is not None}\n",
    "\n",
    "    plt.figure(figsize=(8, 6))\n",
    "    nx.draw(binomial_tree, pos, labels=labels, with_labels=True, node_color='skyblue', node_size=1500, font_color='black')\n",
    "    plt.gca().invert_yaxis()  # Invert y-axis to align the first node at the top\n",
    "    plt.axis('off')  # Turn off axis display\n",
    "    plt.show()\n",
    "\n",
    "mb_binomial_tree_european_call(2, 100, 105, 1, 0.05, 0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2806443d-b398-4289-a082-282e25d4306c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def mb_binomial_tree_european_call(n, S, K, T, r, v):\n",
    "    # Delta time\n",
    "    dt = T / n\n",
    "    # Up and down factors\n",
    "    u = math.exp(v * math.sqrt(dt))\n",
    "    d = 1 / u\n",
    "    # Risk-neutral probability\n",
    "    p = (math.exp(r * dt) - d) / (u - d)\n",
    "\n",
    "    # Initialize stock price tree\n",
    "    stock = np.zeros([n + 1, n + 1])\n",
    "    for i in range(n + 1):\n",
    "        for j in range(i + 1):\n",
    "            stock[j, i] = S * (u ** (i - j)) * (d ** j)\n",
    "\n",
    "    # Initialize option price tree\n",
    "    option = np.zeros([n + 1, n + 1])\n",
    "    option[:, n] = np.maximum(np.zeros(n + 1), stock[:, n] - K)\n",
    "\n",
    "    # Calculate the option price at t=0\n",
    "    for i in range(n - 1, -1, -1):\n",
    "        for j in range(i + 1):\n",
    "            option[j, i] = math.exp(-r * dt) * (p * option[j, i + 1] + (1 - p) * option[j + 1, i + 1])\n",
    "\n",
    "    # Displaying the binomial tree graph\n",
    "    binomial_tree = nx.Graph()\n",
    "\n",
    "    for i in range(n + 1):\n",
    "        for j in range(i + 1):\n",
    "            binomial_tree.add_node((j, i), pos=(i, 2 * j - i - n), value=option[j, i] if j <= i else None)\n",
    "\n",
    "    for i in range(n):\n",
    "        for j in range(i + 1):\n",
    "            binomial_tree.add_edge((j, i), (j, i + 1))\n",
    "            binomial_tree.add_edge((j, i), (j + 1, i + 1))\n",
    "\n",
    "    pos = nx.get_node_attributes(binomial_tree, 'pos')\n",
    "    labels = nx.get_node_attributes(binomial_tree, 'value')\n",
    "    labels = {key: f'{value:.2f}' for key, value in labels.items() if value is not None}\n",
    "\n",
    "    plt.figure(figsize=(8, 6))\n",
    "    nx.draw(binomial_tree, pos, labels=labels, with_labels=True, node_color='skyblue', node_size=1500, font_color='black')\n",
    "    plt.gca().invert_yaxis()  # Invert y-axis to align the first node at the top\n",
    "    plt.axis('off')  # Turn off axis display\n",
    "    plt.show()\n",
    "\n",
    "mb_binomial_tree_european_call(10, 100, 105, 1, 0.05, 0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48e9463b-95c9-44d4-aa90-1295b28542d7",
   "metadata": {},
   "source": [
    "#### Visualizing the put prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ca33c6c2-817e-4cbc-bad5-c9996e70f33b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def mb_binomial_tree_european_put(n, S, K, T, r, v):\n",
    "    # Delta time\n",
    "    dt = T / n\n",
    "    # Up and down factors\n",
    "    u = math.exp(v * math.sqrt(dt))\n",
    "    d = 1 / u\n",
    "    # Risk-neutral probability\n",
    "    p = (math.exp(r * dt) - d) / (u - d)\n",
    "\n",
    "    # Initialize stock price tree\n",
    "    stock = np.zeros([n + 1, n + 1])\n",
    "    for i in range(n + 1):\n",
    "        for j in range(i + 1):\n",
    "            stock[j, i] = S * (u ** (i - j)) * (d ** j)\n",
    "\n",
    "    # Initialize option price tree\n",
    "    option = np.zeros([n + 1, n + 1])\n",
    "    option[:, n] = np.maximum(np.zeros(n + 1), K - stock[:, n])  # Change here for put option\n",
    "\n",
    "    # Calculate the option price at t=0\n",
    "    for i in range(n - 1, -1, -1):\n",
    "        for j in range(i + 1):\n",
    "            option[j, i] = math.exp(-r * dt) * (p * option[j, i + 1] + (1 - p) * option[j + 1, i + 1])\n",
    "\n",
    "    # Displaying the binomial tree graph\n",
    "    binomial_tree = nx.Graph()\n",
    "\n",
    "    for i in range(n + 1):\n",
    "        for j in range(i + 1):\n",
    "            binomial_tree.add_node((j, i), pos=(i, 2 * j - i - n), value=option[j, i] if j <= i else None)\n",
    "\n",
    "    for i in range(n):\n",
    "        for j in range(i + 1):\n",
    "            binomial_tree.add_edge((j, i), (j, i + 1))\n",
    "            binomial_tree.add_edge((j, i), (j + 1, i + 1))\n",
    "\n",
    "    pos = nx.get_node_attributes(binomial_tree, 'pos')\n",
    "    labels = nx.get_node_attributes(binomial_tree, 'value')\n",
    "    labels = {key: f'{value:.2f}' for key, value in labels.items() if value is not None}\n",
    "\n",
    "    plt.figure(figsize=(8, 6))\n",
    "    nx.draw(binomial_tree, pos, labels=labels, with_labels=True, node_color='skyblue', node_size=1500, font_color='black')\n",
    "    plt.gca().invert_yaxis()  # Invert y-axis to align the first node at the top\n",
    "    plt.axis('off')  # Turn off axis display\n",
    "    plt.show()\n",
    "\n",
    "mb_binomial_tree_european_put(2, 100, 105, 1, 0.05, 0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7748244d-2ec8-4b83-91ef-590ca56e1b6f",
   "metadata": {},
   "source": [
    "#### American Options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1a937461-4586-41eb-91af-7b5bc9a1239f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "American call\n",
      "8.081246948239023\n",
      "American put\n",
      "9.088257638650122\n"
     ]
    }
   ],
   "source": [
    "def mb_binomial_tree_american(n, S, K, T, r, v, otype='call'):\n",
    "    dt = T/n\n",
    "    u = math.exp(v * math.sqrt(dt))\n",
    "    d = 1/u\n",
    "    p = (math.exp(r*dt) - d)/(u - d)\n",
    "    \n",
    "    # Price tree\n",
    "    price_tree = np.zeros([n+1, n+1])\n",
    "    \n",
    "    for i in range(n+1):\n",
    "        for j in range(i+1):\n",
    "            price_tree[j, i] = S * (u ** (i - j)) * (d ** j)\n",
    "\n",
    "    # Option value\n",
    "    option = np.zeros([n+1, n+1])\n",
    "\n",
    "    # Calculate the option price at expiration\n",
    "    if otype == 'call':\n",
    "        option[:, n] = np.maximum(np.zeros(n+1), (price_tree[:, n]-K))\n",
    "    elif otype == 'put':\n",
    "        option[:, n] = np.maximum(np.zeros(n+1), (K - price_tree[:, n]))\n",
    "    else:\n",
    "        raise ValueError(\"Invalid option type. Please use 'call' or 'put'\")\n",
    "\n",
    "    # Calculate option price at t=0\n",
    "    for i in range(n-1, -1, -1):\n",
    "        for j in range(0, i+1):\n",
    "            if otype == 'call':\n",
    "                exercise = np.maximum(price_tree[j, i] - K, 0)\n",
    "            elif otype == 'put':\n",
    "                exercise = np.maximum(K - price_tree[j, i], 0)\n",
    "            \n",
    "            no_exercise = math.exp(-r * dt) * (p * option[j, i + 1] + (1-p) * option[j + 1, i + 1])\n",
    "            option[j, i] = np.maximum(exercise, no_exercise)\n",
    "    \n",
    "    return option[0, 0]\n",
    "\n",
    "# Testing the function with an American call\n",
    "print(\"American call\")\n",
    "print(mb_binomial_tree_american(2, 100, 105, 1, 0.05, 0.2, 'call'))\n",
    "\n",
    "# Testing the function with an American put\n",
    "print(\"American put\")\n",
    "print(mb_binomial_tree_american(2, 100, 105, 1, 0.05, 0.2, 'put'))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc055433-b595-455c-bd6d-b13b9cc02ed5",
   "metadata": {},
   "source": [
    "## Trinomial Tree Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f139ad96-ce51-4f97-8076-d7885b94b244",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "European call\n",
      "7.912118772905886\n",
      "European put\n",
      "7.7915021374046916\n"
     ]
    }
   ],
   "source": [
    "def mb_trinomial_tree_european(n, S, K, T, r, v, otype='call'):\n",
    "    # Calculating delta T\n",
    "    dt = T/n\n",
    "\n",
    "    # Parameters for trinomial tree\n",
    "    dx = v * math.sqrt(3 * dt)\n",
    "    nu = r - 0.5 * v**2\n",
    "    pu = 0.5 * ((v**2 * dt + nu**2 * dt**2) / dx**2 + nu * dt / dx)\n",
    "    pd = 0.5 * ((v**2 * dt + nu**2 * dt**2) / dx**2 - nu * dt / dx)\n",
    "    pm = 1 - pu - pd\n",
    "\n",
    "    # Initialize arrays for storing stock prices and option values\n",
    "    stock_price = np.zeros((2*n+1, n+1))\n",
    "    option_value = np.zeros((2*n+1, n+1))\n",
    "\n",
    "    # Calculate stock prices\n",
    "    for i in range(-n, n+1):\n",
    "        stock_price[i, :] = S * np.exp(i * dx)\n",
    "\n",
    "    # Calculate option values at maturity\n",
    "    if otype == 'call':\n",
    "        option_value[:, n] = np.maximum(stock_price[:, n] - K, 0)\n",
    "    elif otype == 'put':\n",
    "        option_value[:, n] = np.maximum(K - stock_price[:, n], 0)\n",
    "\n",
    "    # Perform backward iteration to find option value at t=0\n",
    "    for j in range(n-1, -1, -1):\n",
    "        for i in range(-j, j+1):\n",
    "            option_value[i, j] = math.exp(-r * dt) * (\n",
    "                pu * option_value[i+1, j+1] + \n",
    "                pm * option_value[i, j+1] + \n",
    "                pd * option_value[i-1, j+1]\n",
    "            )\n",
    "    return option_value[0, 0]\n",
    "\n",
    "# Testing the function with a European call\n",
    "print(\"European call\")\n",
    "print(mb_trinomial_tree_european(2, 100, 105, 1, 0.05, 0.2, 'call'))\n",
    "\n",
    "# Testing the function with a European put\n",
    "print(\"European put\")\n",
    "print(mb_trinomial_tree_european(2, 100, 105, 1, 0.05, 0.2, 'put'))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6b22a4f4-f1e0-4d43-82eb-1bc920dbfc3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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RFadNlMfr1dO/vkV7d32qOX9a3O7z/GXu+Rp+ypmadNUNnb7m208/qhUP/E43LF0twzDUuLtOd884Q+f96Bc6cfK3lIjFVLRvp246Z0JGf1bALZjb9HDGCUDGDP7auToqYapm/VrV14ZbPn/M6ZNbfd1pl35Pf5l7frvPsXt7tba885Zm/PyPKb3mmspFGnPeJS0bVL6+4F5VnHaWxpw7Q5LkCxTI36tnV34cIC8wt+mxX3kIwJH2xRIp38q8ec2bOnLYse0+tqZysYaMOVVH9B/c6fPs3r5Nm9e8qbFTL2n5XPV7b6tHaW/dGzxX/3fScXrwB5dpV802NVi1OQ1gY8xt+ghOADJiVzghXwpvS7LjHx9oxf2/1TnX/6zdx9dULtLJ3/p2Sq+55pm2B+v62u1as2yRpt54h25e/o769B+kR//t+6oNx1P7QYA8wtymj+AEICOiCVNmJ/flfFb9sULXfVtTb7hDQ8ee1ubxLe+8pYa6Wp0w+VspveY7lYs0duqlrT7nLyjS8Wedq4HHj5G/oFCTrrpRW95drbrde1L+WYB8wdymj2ucAGREopP7THZv36a/zpuhiXN/1OoU/cHWVC7S8ROnqqBH52/0uWXtKu3dtVMnTp7W6vNHVYyUDvoNuvkaijlXXqn3X1jW6fMC+WT0OdN1/o/vUmFx+9cTWT238SRVHQCX8hqGEvG4YpEmJZMJJRNJxSJNSsTjqq/doQeuvkinXTJHE2YE2/3+WFNY7/3t6dRP9y9bpBMmTVVBceuD9bhp39EHLy3X9o/eUyIW04r7f6uhYybo8cWPyzRNPvjg46CPRxcuVHFRkW3ntk/vPik9by5xxglARgS8hl64/3d6/s93tXxu7fLHNemqGyXD0OefbNGLf7lLL/7ly8dvW7m15c8fvPysCkt6adgpZ7R57rtnnKF/nnN9yx03sUiT3vvbUl121/w2Xzt8/Jn65rW36sF/+a6iTWENGT1BM3/1FwW8nV/HAeQb5jZ97OMEICP2xRK674PdtnnbhoN5DWne8UeoxM9JduBgzG367LUaAI7V0++Vz2O/3w4lyecxbHfwBeyAuU2f/VYEwLHKAvY8AJcX8j51wOEwt+nhGicA3WKapt544w2FQiFVe0r1tTk/lDdQYPWyWsSawnr+qUWKDinTjBkz1LOnPXcjBnLJNE29+eabCoVC2mr0st3c+gxpRGnA6mW0izNOALqkurpad9xxh44++mhdeeWVqqio0L0/+VcFCuxz8JWkwqIiTTv5WC1dulQDBw7U7Nmz9dJLLylpw9ucgWzbtm2bfvnLX+qYY47RnDlzNGzYMP3nrdfbbm5NSaPKCq1eRru4OBxAyvbv368nn3xSoVBIa9as0aWXXqpgMKhTTjmlZd+Vpzbv1Ud7op1sqZcbhqRjegd0wdBekqTa2lotXLhQ8+fP1969ezV79mzNmjVLw4cPt3ahQBbt379fTz31lEKhkP7+97/rkksuUTAY1IQJExwxt3ZDcALQoYOruCVLlujUU09VMBjUtGnTVFjY9jfC7Y0xPVJVr7gNjiw+Q7qsolR9i/2tPm+aptauXatQKKRHHnlEI0eOVDAYpMqDaxxcxT3xxBMaP368gsGgzj//fBUVFbX5eifMrV0QnAC0q7q6Wg8//LBCoZB8Pp+uuOIKzZw5U/369ev0e5/8eK827o1aeouz94trJC7s5LfWaDSq5cuXKxQK6eWXX9b555+vYDCor3/96/J4uJoBzrJt27aWufV4PAoGg5o5c6YGDBjQ6fc6aW6tRHAC0CKVKi4V4XhS963frYiFR+ACr6F5I/uo0Jd6+KHKgxOlUsWlwqlzm2sEJyDPpVvFpaqqPqKnt+xTzIJrsP0eadqQnqoo7doFr1R5sLt0q7hUOXluc4XgBOSp7lRxqXrxkwatrWvK6UHY75FGlxVq0oDO33A0FVR5sJPuVHGpcsPcZhPBCcgjmariUmWapp6tbtCGPZGcHIT9Hmlk7wJNGVSSlZ+HKg9WyFQVlyq3zW2mEZwAl8tWFZfO66+oacz6b7DNv7FO7F+c9YMvVR6yLVtVXDqv77a5zRSCE+BSuaji0lFVH1Hl1gbFk2ZG79rxGgfe02rq4BJLro2gykMm5aKKS4db57Y7CE6Ai+S6iktXOJ7Uc9UN2vTFLc/dOfgYOnDwHV4a0JSBJSqywV04VHnoilxXcely+9ymi+AEOJzVVVxX7GiMaVVtWFX1URlSWpvu+YwDB+6K0oAmlBfZcpM8qjx0xuoqrivcPrepIjgBDmW3Kq4rwvGk1tU1aWN9VLVNCcWTpnyGIVOmTB347dSQobhpyucxVF7o1YjSgEaVFTrmN1WqPBzMblVcV+TD3HaE4AQ4iN2ruO5qiCVVG44rmjCVME15DUMBr6HyIp9K/M4/4FLl5Se7V3Hd5fa5PRTBCbA5J1Zx6BhVnvs5sYpDaghOgE0dWsUFg0Fdfvnljqri0LloNKpnnnlGoVBIr7zyClWew7mhikPHCE6AjRxaxTWf0h8/frwrTumjYzt37tQjjzxClecwbq/i0BrBCbAYVRwORZVnf1Rx+YvgBFiEKg6poMqzF6o4EJyAHKKKQ3dQ5VmDKg4HIzgBWUYVh0yjyss+qjgcDsEJyBKqOOQCVV5mUcWhMwQnIIOo4mAlqryuoYpDOghOQDdRxcFuqPI6RxWHriI4AV1EFQcnoMprjSoO3UVwAtJAFQcny9cqjyoOmURwAjpBFQe3yYcqjyoO2UJwAg6DKg75wG1VHlUcso3gBByEKg75zKlVHlUcconghLxHFQe05oQqjyoOViE4IW9RxQGds1uVRxUHqxGckFeo4oCus6rKo4qDnRCc4HpUcUBm5aLKo4qDXRGc4FpUcUD2ZbrKo4qD3RGc4CpUcYB1ulrlUcXBSQhOcDyqOMBeUqnyqOLgVAQnOBZVHGB/h1Z5kydPVu/evfXKK6/I6/VSxcFxfFYvAEhHe1XcggULqOIAmwoEAvrmN7+pcDisPXv2aPny5SoqKlIgENDcuXN18cUXE5rgKM7bTx95xzRNrVy5UnPnzlX//v21YMECXXnllaqpqdG9997LdRCADTVX6FdddZUGDBighx56SPPmzVNdXZ0+++wzLV++XPX19Tr11FP19a9/XfPnz9e+ffusXjbQKao62FZ7VdzMmTPVv39/q5cG4DDSvSvObhtsAp0hOMFWuCsOcJ5M3RXn1PfKQ34hOMFyB98V98QTT7TcFXf++edzVxxgU9m8K84J75WH/EVwgmWo4gDnyfUGlVR5sBuCE3KKKg5wHrtsUEmVBzsgOCHrqOIA57HzBpVUebASwQlZQxUHOI/T3iuOKg+5RnBCRlHFAc5jlyquu6jykAsEJ3QbVRzgPHau4rqLKg/ZRHBCl1HFAc7jtCquu6jykGkEJ6SFKg5wHrdUcd1FlYdMIDihU1RxgPO4uYrrLqo8dAfBCYdFFQc4T75Vcd1FlYd0EZzQClUc4DxUcZlBlYdUEJxAFQc4EFVc9lDloSMEpzxGFQc4D1VcblHl4VAEpzxDFQc4D1WcPVDlQSI45QWqOMB5qOLsiyovvxGcXIwqDnAeqjhnocrLPwQnl6GKA5yHKs4dqPLyA8HJBajiAOehinMvqjx3Izg5GFUc4DxUcfmFKs99CE4OQxUHOE84HG6ZW6q4/NVelTd79mwNGzbM6qUhDa4NTvtiCe0KJxRNmEqYpryGoYDXUHmRTyV+Z6X8g6u4JUuWaMKECVRxcCW3ze1bb72lUCikxx9/nCoOLdxW5blpblPhmuAUjie1rq5JG+ujqm1KKJ405TMMmfryxzNkKG6a8nkMlRd6NaI0oFFlhSry2fMflioObufGuaWKQzqcWOW5cW7T4fjgtL0xptW1YVXVR2VIiqfx0/gMyZRUURrQ+PIi9Sv2Z2uZKaOKQz5w29xSxSET7F7luW1uu8qxwSkcT+q56gZt2htVwpS680MYkryGNLxXQFMGleQ8EVPFIV+4bW6p4pANdqvy3DS3meDI4FRVH1Hl1gbFk6YSGVy915B8HkNTB5eoorQgc098GFRxyCdumVuqOOSS1VWeW+Y2kxwVnEzT1IqaRq2ta1Ismb3X8Xuk0WWFmti/OOOn2anikG/cMLdUcbCDXFZ5bpjbbHFMcDJNU89WN2jDnkhW/xGb+T3Scb0LdM6gkm7/Y1LFIV85fW6p4mBH2a7ynDy3ueCY4PTiJw1ZT76Hak7CkwaUdOn7qeKQ75w4t1RxcJJsVHlOnNtcckRwqqqP6Okt+3L6j9jM75GmDemZcgdLFQcc4KS5pYqDG2SiynPS3FrF9sEpHE/qvvW7FcnkVWlpKvAaunpkn8Ne/U8VB7TmlLmlioMbdbXKc8Lc2oHtg9OTH+/Vxi9ugbSK15BGlAZ04dBerT5PFQe0z85zSxWHfJJOlWfnubUTWwen7Y0xPVJVn9YmW9niM6TLKkpVasSo4oAO2HFue3viVHHIex1VeXac27423STT1sHpqc179dGeaLc228oY09S+jet079UXU8UBHbDb3DZsek//+f0ZVHHAF9qr8i742R8V7dPfFnNrSDqmd0AX2PSsk22DUzie1D3vf27pKcM2EnFdcmRCwwZSxQHtsevcXlwe1/BBVHHAoaLRqJ5+9n/0j74ny+MPWL2cFl5DuvaEI2x5rZP9VvSFdXVNstsJdJ/Pp12BPlYvA7Atu87tZwVHWL0MwJYCgYAGnjpJgYB9QpN04KzTuromq5fRLtsGp//80z36/Xcn698n9NfjP7u21WMbV72q3110mn761UG6/6oLtHv7tpbHTNPUs3+4XbefdbRuP+toPfv729TRSbV0nmvZ3bepak8k8z8s4BLMLeA8zG16bBucPL2P1FlX/qvGnf/dVp9v3F2nBTcGdfa8W/STl/6h/seN1qO3zG15fPWSh7T+5eX6wWMv6weLXtGHrz2v1UsebPc1uvJcSx/+a3Z+YMAFmFvAeZjb9NgyOO2LJTRy4nk6/qxz1aO0dTX2wYpndOSwY3Xi2efLX1CoyVffqB1VH6h2c5UkaU3lIp058xqVHtlPpeV9dcbl8/T204+1+zpdea7VTz+mBit2BgNsjrkFnIe5TZ8tg9OucEK+w9wivPPjD9X36ONb/h4oKlbZgCGq/fjDlsePOujxvkefoJ1fPJaR59r0oWrD8a7/cIBLMbeA8zC36bNlcIomTJmHuSkyur9RhSWtdz4tLOmpSGPDQY/3avVYdH9ju71rV54rsr9Rkbj9EjBgNeYWcB7mNn0+qxfQnkQHF5cFehSr6Yv/0M2aGhtUUFzS8nikcV/LY5GGBgV6FLe7yV2XnquoWN+dOVNrn12S/g8GuNjoc6br/B/fpcLitm/pwNwC9mTnuS3oUSz7xSabnnHydrCT75HDjtWn/3i/5e/RcKM+/2SLyocd2/L4jn980PL4jn+8ryO/eCwTz3XUiGP16MKFMk2TDz74OOjj0YUL1esw74PF3PLBhz0/7Dy3Rw4/tsM8YBVbBqeA11AynlAs0qRkMqFkIqlYpEmJeFwjJ56rTzd9qPdfXKZYpEkv/uW3OmrESJUPrZAkjZ16iV5fcK/qa3do765P9dqCe3XytG+3+zpdea7x076tgNd+/5CA1ZhbwHmY2/TZcufwfbGELrru3/TCn+9q9flJV92oyVffpI2rXtHTv75Fu3d8ooEnjNXFt/0/9ek3SNKBvSCe+8Pt+t+nFkiSTrlgpqb84Kctpw7vnnGG/nnO9Rpz7gxJSvu5zrv+p7rmhDKV+G2ZOQHLMLeA8zC36bNlcJKku9fVKWKr9204oMBr6IejyqxeBmBLzC3gPMxteuwV4w5SXui1egntsuu6ADuw63zYdV2AHdh1Puy6LtsGpxGlAflsVm3GImFtXv2KtmzZYvVSAFuy7dyuelmbN2+2eimArYTDYT322GN6afGDijWFrV5OKz7jwPHEjmwbnEaVFR5mZwnrFAQKVPvO6xo3bpwmTpyohx56SI2NjVYvC7ANu87trnVvavz48TrrrLP04IMPqqGhofNvBFzINE299dZbuvrqqzVgwAD913/9l75e0U+FRUVWL60VUweOJ3Zk2+BU5POoojRgm3daNyQd3adQf/ztXaqpqdE111yjxYsXa8CAAZozZ45effVV2fRyMSBn7Dq3f7jr1/rkk0903XXXacmSJRo4cKCuuOIKvfLKK0om7bhTDJBZNTU1uvPOO3Xcccdp1qxZGjRokNauXavnn39el196se3mtqI0oCKfPSOKbS8Ol6TtjTE9UlWvuA1W6DOkyypK1bfY3+rzO3bs0MKFCzV//nw1NTVp9uzZmjVrloYMGWLNQgGLOWFud+7c2TK3jY2NLXM7dOhQi1YKZF44HNbSpUsVCoW0evVqzZgxQ8FgUKeddlqbTSqdMLd2YevgJElPfrxXG/dGZeUF/94vutYLh/Y67NeYpqm3335boVBIjz32mEaNGqVgMKjp06eruLg4h6sFrOekuX3nnXcUCoX06KOP6oQTTmiZ25KSkhyuFsgM0zS1atUqhUIhPf744zr55JMVDAZ1wQUXqEePHh1+r1Pm1mq2D07heFL3rd9t6a2SBV5D80b2UWGKpw0jkYiWLVumUCiklStX6sILL1QwGNSZZ57Z7lb0gNs4dW6feeYZhUIhvfbaa7rgggta5tbjsWdlADSrqanRww8/rFAopGQyqWAwqMsvv1wDBw5M+TmcOLdWsH1wkqSq+oie3rJPMQsuRfB7pGlDeqqitKBL30+Vh3zl5LmlyoMTpFPFpcrJc5srjghOkvTiJw1aW9eU039Mv0caXVaoSQO6f8qeKg/5yA1zS5UHO+lOFZcqp89ttjkmOJmmqWerG7RhTyQn/5h+jzSyd4GmDCrJeL1GlYd84ba5pcqDVTJRxaXKTXObDY4JTtKBf8wVNY1ZT8LNyXdi/+Ks/yNS5cHt3Di3VHnIhWxUcaly49xmiqOCU7Oq+ogqtzYonjQzevW/15B8HkNTB5fkvGOlyoPbuXVuqfKQSbmo4tLhxrntLkcGJ+nA1f/PVTdo0xe3TnbnhzB04B9xeGlAUwaWWL7pFlUe3Mrtc0uVh67KZRWXLjfPbVc4Njg129EY06rasKrqozKktDbv8hkH/gdQURrQhPIiW262RZUHN3L73FLlIRVWVnFd4fa5TZXjg1OzcDypdXVN2lgfVW1TQvGkKZ9hyJQpUwdSriFDcdOUz2OovNCrEaUBjSordETipcqDG+XD3FLl4WB2q+K6wu1z2xnXBKdDNcSSqg3HFU2YSpimvIahgNdQeZFPJX5n/8NR5cGt3D63VHn5y85VXHe5eW7b49rglC+o8gDnocrLD06r4pAagpNLUOUBzkOV5z5uqOLQMYKTC1HlAc5Dledsbq7i0BrByeWaq7xQKKRwOEyVBzgAVZ4zUMXlJ4JTnqDKA5yHKs9+qOJAcMpDVHmA81DlWYsqDs0ITnmOKg9wHqq83KCKQ3sITpBElQc4EVVe5lHFoTMEJ7RBlQc4D1Ve91DFIVUEJ3SIKg9wHqq81FDFoSsITkgJVR7gPFR5bVHFobsITkgbVR7gPPle5VHFIVMITugWqjzAefKlyqOKQzYQnJARVHmA87ixyqOKQ7YRnJBxVHmA8zi9yqOKQ64QnJBVVHmA8zilyqOKgxUITsgJqjzAeexY5VHFwWoEJ+QcVR7gPFZXeVRxsAuCEyxFlQc4T66qPKo42BHBCbZAlQc4TzaqPKo42B3BCbZDlQc4T3erPKo4OAXBCbZGlQc4T6pVHlUcnIjgBEegygOcp70qb/bs2Ro0aJAWL15MFQdHIjjBcajyAOf5+OOP9dOf/lRPPfWUwuGwRo8erVtuuUXTp093xAabQDP+1wrHKSgo0IwZM1RZWan169dr5MiRuuaaazRixAjdfvvt2rp1q9VLBKADVdxjjz2mKVOmaNy4cerRo4eef/551dTU6LLLLtPtt9+uESNG6LbbbtPmzZutXi6QEs44wRUOrfJOOukkBYNBXXTRRVR5QA4delfcuHHjWqq4oqKiNl9rtw02gc4QnOA6VHlA7nX3rjirN9gEUkVwgqu1d1fe7NmzNXjwYKuXBjhetu6Kc8p75SE/EZyQF6jygMxIp4rLxGtR5cFuCE7IO1R5QPqs3qCSKg92QXBCXqPKAw7PrhtUUuXBSgQnQFR5QLNcVnHdRZUHKxCcgENQ5SEfWV3FdRdVHnKF4AR0gCoPbmbXKq67qPKQTQQnIAVUeXALJ1Vx3UWVh2wgOAFposqDEzm9iusuqjxkCsEJ6AaqPNiZW6u47qLKQ3cQnIAMoMqDXeRTFdddVHnoCoITkGFUebBCvldx3UWVh1QRnIAsospDNlHFZQdVHjpCcAJygCoPmUIVlztUeWgPwQnIMao8dAVVnLWo8tCM4ARYiCoPHaGKsyeqvPxGcAJsgCoPzajinIMqLz8RnACbocrLT1RxzkaVlz8IToCNUeW5G1WcO1HluRvBCXAAqjz3oIrLH1R57kRwAhwmEomosrJSoVBIr7/+ui666CIFg0GdccYZnKWwsYOrONM0FQwGNXPmTKq4PEGV5x4EJ8DBPv30Uy1YsKClygsGg5o1a5Zjq7x9sYR2hROKJkwlTFNew1DAa6i8yKcSv/P+z6Wpqamlilu1apUuvvhiBYNBnXrqqYTcPOa2Ks9tc9sZghPgAk6t8sLxpNbVNWljfVS1TQnFk6Z8hiFTXx6WDBmKm6Z8HkPlhV6NKA1oVFmhinz2PCBTxSFVTq3y3Di36SA4AS7jhCpve2NMq2vDqqqPypAUT+Mo5DMkU1JFaUDjy4vUr9ifrWWmhSoO3eGEKs+Nc9sVBCfAxexW5YXjST1X3aBNe6NKmFJ3Dj6GJK8hDe8V0JRBJZb8JksVh2ywW5XntrntLoITkAfsUOVV1UdUubVB8aSpRAaPOl5D8nkMTR1coorSgsw98WFQxSFX7FDluWVuM4ngBOSZXFd5pmlqRU2j1tY1KZbM+NO38Huk0WWFmti/OCs/B1UcrJTrKs8tc5sNBCcgj2W7yjNNU89WN2jDnkhWD77N/B7puN4FOmdQSUYOwlRxsKNsV3lOn9tsIzgByFqV9+InDVn/jfVQzb/BThrQtSqDKg5Oka0qz4lzm0sEJwCtZKrKq6qP6Okt+3J68G3m90jThvRM69oJqjg4WaaqPKfNrRUITgAOq6tVXjie1H3rdyuSyatJ01TgNXT1yD4d3rVDFQc36mqV55S5tRrBCUCn0q3ynvx4rzZ+ceuyVbyGNKI0oAuH9mr1eao45It0qzw7z62dEJwApKWzKm97Y0yPVNWntTletvgM6bKKUvUt9lPFIa91VuXZdW7tiOAEoMvaq/KGXThXn8R83dokL1MMSUV7P9Wzd95IFQd8ob0qb8T0q/RJzG+buT2md0AX2PSsE8EJQLc1V3kPPbpI5Rf/QL6CQquX1CIRi2rw5jc0fdp5VHHAQZqrvAcfXaSvTL/OVnPrNaRrTzjCltc6EZwAZMyqnfv12o79tjjd38xnSGf27aEJR/aweimALTG36fFZvQAA7rGxPtpy8P3Z6a3vvItFmnTqxVdo2s13SpLWPf+UXrjvN6qv3a7eR/bXN669VcefdW6b54xHI1r6q5u0cdWr2r93t8oGDtU3r71Vx5w+WZL0zvIn9NQdP2r5etM0FWsK69oFL6j/yJMUNw+sy44HYMAOmNv0EJwAZExtU6Llz7et3Nry52i4UXdMHqkTJ0+TJNXX7tDif79Gl9/9kI7+6iR99Prf9MjNV+qmyrdVcsRXWj1nMhFX6ZH9ddUDS1V61AB99PoLeuTmK3X94lfVp98gjTl3hsacO6Pl699++lGteOB36nfcqHbXBaA15jY99isPATjSvlhC8WT75/rfe2GZio/4ioaMPU2SVL9zuwp7luqY0yfLMAwde+Y3FCjsobptW9p8b6CoWJOvvkl9+g2Sx+PRcV/7ho7oN1g1G95t97XWVC7SmPMuaXXxdzxpqsGKHf0Am2Nu00dwApARu8IJ+Q5zp9qaZYs09qCD4oCRo1U+tELrX3lOyURCH7y0XN5AQH2PHtnp6+yrq9Vn1ZtUPuzYNo/t3r5Nm9e8qbFTL2n1eZ9hqDYc78JPBbgbc5s+qjoAGRFNmDLbuZl5z45PtHnNG5r+s9+3fM7j9WrM1Eu06MffVzwakdcf0Hd//YACRR2/L14iFtOiW+dp7NRLVT60os3ja55ZrCFjTtUR/Vtfp2HKVNTKXf0Am2Ju08cZJwAZkTjMDbprnlmkIaMntDooblz1ip79w+2ae/9S/WLVds29f6n++xc/1PaP3jvs8yeTSS3+yTXy+v0tF6oe6p3KRRo79dI2n9+7b5++c9llMgyDDz74OOjjO5ddpr379tlybk0d/rhiJc44AcgIr3GY0/2Vi/XPwX9p9bntH72voWNP04CRoyVJA48fo4EnnKyNq15Vv2NObPMcpmnqv2/7gRo+36XgHx+V1992R+Eta1dp766dLReyHqxXz556dOFCHdvniS78ZIB7fbg7ouXV+xQ95FIiO8ytocMfV6zEGScAGRHwGjLU+iC39d3V2lv7qU48+/xWnx9w/Ghteeetlt9Ut3+4TpvfeUtHVbR/rcRTv7xRtZurNOv3C+QvbH8TyzXLFumESVNVUNz2PbgMGQp47XcABqzG3KaPM04AMuIrRV7FDzmtvmbZIh0/8bw2B8VhJ5+uSVfdqIU3zlHD57tU3OefdNac63X0aWdJkl76693a8s5buuKeRdq9fZtWL3lQvkCBfnn28S3PccGtv225nTkWadJ7f1uqy+6a3+7a4qap8iIOd8ChmNv0sXM4gIy5e12dIja8mLPAa+iHo8qsXgZgS8xteqjqAGRMeaHX6iW0y67rAuzArvNh13URnABkzIjSgHw2uyQhGYvK+3mNOLkOtM+Oc+szDqzLjghOADJmVFlhOzvCWMvj8eg318/ViBEj9Itf/EJbt27t/JuAPGLHuTV1YF12RHACkDFFPo8qSgOyyy+vhqRjy3ro7TdXatGiRdq5c6dOPvlkTZo0SQ8//LAaGxutXiJgOTvObUVpQEU+e0YUe64KgGONLy+SXe4g9hrShPIiGYahcePG6Z577lFNTY2uueYaLV68WAMGDND3vvc9vfbaa1R5yGt2nFu7IjgByKh+xX4N7xWw/CDsNaThpQH1LW696V5BQYGmT5+uZcuWacOGDTruuOM0b948qjzkNbvPrZ0QnABk3JRBJfJ5rD0C+zyGzhnYdlO9gx111FG64YYb9N5771HlIe85ZW6txj5OALKiqj6ip7fsUyzZ+ddmmt8jTRvSUxWlBWl/byQSUWVlpUKhkF5//XVddNFFCgaDOuOMM2TY8O0fgExy6tzmEsEJQNa8+EmD1tY15fQg7PdIo8sKNWlA939r/fTTT7VgwQKFQiGFw2EFg0HNmjVLgwcP7vybAYdy+txmG8EJQNaYpqlnqxu0YU8kJwdhv0ca2btAUwaVZPTskGmaevvttxUKhfTYY4/ppJNOUjAY1EUXXaTi4uKMvQ5gB26Z22whOAHIKtM0taKmMeu/wTb/xjqxf3FWD75UecgHbpvbTCI4AciJqvqIKrc2KJ40lcm3xfIaBy4onTq4JOfXRlDlwe3cOLfdRXACkDPheFLPVTdo096oEqa6tVuxoS9vXZ4ysMTSzfKo8uBmbp3briI4Aci5HY0xraoNq6o+KkNSPI2jkM84cOCuKA1oQnmR7fZ7ocqDW7l5btNBcAJgmXA8qXV1TdpYH1VtU0LxpCmfYciUKVMHfjs1ZChumvJ5DJUXejWiNKBRZYWO+E2VKg9u5Pa57QzBCYBtNMSSqg3HFU2YSpimvIahgNdQeZFPJX7nHnCp8uBmbp3bwyE4AUAOHVrlXXjhhQoGgzrzzDOp8gAHIDgBgEUOrfJmz56t2bNnU+UBNkZwAgCLUeUBzkFwAgAbiUQiWrZsmUKhkFauXEmVB9gMwQkAbGrHjh1auHAhVR5gIwQnALA5qjzAPghOAOAgVHmAtQhOAOBQVHlA7hGcAMDhqPKA3CE4AYCLUOUB2UVwAgCXosoDMo/gBAAuR5UHZA7BCQDyCFUe0D0EJwDIU1R5QPoITgCQ56jygNQRnAAALajygI4RnAAA7aLKA9oiOAEAOkSVB3yJ4AQASBlVHvIdwQkA0CVUechHBCcAQLdQ5SGfEJwAABlDlQe3IzgBALKCKg9uRHACAGQVVR7chOAEAMgZqjw4HcEJAGCJ9qq8WbNmaciQIVYvDTgsghMAwFKHVnmjRo1SMBjU9OnTqfJgOwQnAIBtUOXB7ghOAABbosqDHRGcAAC2RpUHOyE4AQAcgyoPViM4AQAciSoPViA4AQAcjSoPuURwAgC4BlUeso3gBABwJao8ZAPBCQDgalR5yCSCEwAgb1DlobsITgCAvESVh64gOAEA8hpVHtJBcAIA4AtUeegMwQkAgHZQ5aE9BCcAADpAlYeDEZwAAEgRVR4ITgAAdAFVXn4iOAEA0A1UefmF4AQAQIZQ5bkfwQkAgCxorvLmz5+vpqYmqjyXIDgBAJBFVHnuQnACACBH3Fjl7YsltCucUDRhKmGa8hqGAl5D5UU+lfg9Vi8v4whOAABYwKlVXjie1Lq6Jm2sj6q2KaF40pTPMGTqyzhhyFDcNOXzGCov9GpEaUCjygpV5HN+kCI4AQBgIadUedsbY1pdG1ZVfVSGpHga6cFnSKakitKAxpcXqV+xP1vLzDqCEwAANmHHKi8cT+q56gZt2htVwpS6ExoMSV5DGt4roCmDShx5BorgBACADdmhyquqj6hya4PiSVOJDKYFryH5PIamDi5RRWlB5p44BwhOAADYmBVVnmmaWlHTqLV1TYols/ISkiS/RxpdVqiJ/Ysdc3E8wQkAAIfIRZVnmqaerW7Qhj2RrIamZn6PdFzvAp0zqMQR4YngBACAA2Wrynvxk4asn2k6VPOZp0kDSnL3ol1EcAIAwMEyWeVV1Uf09JZ9OQ1NzfweadqQnra/5ongBACAS3SnygvHk7pv/W5FMnkVeJoKvIauHtnH1nfbEZwAAHChdKu8Jz/eq41fbDlgFa8hjSgN6MKhvaxbRCfsG+kAAECX9e3bVzfccIPef/99LVq0SLW1tRo3bpwmTpyohx56SI2NjS1fu70x1rJPk5USprSpPqodjTFrF9IBzjgBAJAnDlflfT5wtD7aE+3W5paZYkg6pndAF9j0rBPBCQCAPNRc5S18fImm//EJ+QL2uSjba0jXnnCELa91IjgBAJDH3trZqFdrGpU07BNSfIZ0Zt8emnBkD6uX0obP6gUAAADrbKqPtQlN7/7Pk3rxz3dpz6c16vlP5Zrx8z9q4Ikna9GPv69P1r+rPTu2ae5fntKwcae3+5zxaERLf3WTNq56Vfv37lbZwKH65rW36pjTJ0uS3ln+hJ6640ctX2+apmJNYV274AX1H3mS4qa0sT5KcAIAAPZS25Ro9feqt17Wc3+4Xd+5834NOGGs9n22s+WxwaMn6PTvfl+P3Py9Dp8zmYir9Mj+uuqBpSo9aoA+ev0FPXLzlbp+8avq02+Qxpw7Q2POndHy9W8//ahWPPA79Ttu1GHXZRcEJwAA8tS+WELxZOsrdl647zeaeNWPNGjUOElSaXnflsfOuOxqSZLh8Xb4vIGiYk2++qaWvx/3tW/oiH6DVbPhXfXpN6jN16+pXKQx513Saq+peNJUQyypEr99KkSJ7QgAAMhbu8IJ+Q4KK8lEQjXr16pxd53umnaKfjVllJbeebNiTeFuvc6+ulp9Vr1J5cOObfPY7u3btHnNmxo79ZJWn/cZhmrD8W69bjYQnAAAyFPRhCnzoE0IGj7fpUQ8pvdfWKbv/3WZ/uXRl7Tjo/e04oHfdfk1ErGYFt06T2OnXqryoRVtHl/zzGINGXOqjug/uNXnTZmKWr2xVDsITgAA5KnEITfW+wsKJUmnfftK9frKUSruU6YzZs7TRytf6NLzJ5NJLf7JNfL6/Zp2853tfs07lYs0duqlbT5vtrM+O+AaJwAA8pT3kPevK+rVW6VH9uv0fe1SYZqm/vu2H6jh810K/vFRef3+Nl+zZe0q7d21UydOntbmMaOd9dkBZ5wAAMhTAa8hQ63DycnTvqM3HntADZ/vUnjvHq1c+Gcde+Y3JB3YZiAWaTrw51hUsUiTDrcd5FO/vFG1m6s06/cL5C8savdr1ixbpBMmTVVBcUmbxwwZCnjtF5zYABMAgDy1L5bQfR/sbvUedYlYTMv+41a9++wS+QoKdOLZ5+ucH/xM/oJC/fq8sdqzY1ur57ip8m316TdIL/31bm155y1dcc8i7d6+Tb+ZOla+QIE83i/vwLvg1t+2bEMQizTpl2cfr8vumq8RE77WZm1eQ5p3/BG2u6uO4AQAQB67e12dIja8CLvAa+iHo8qsXkYb9opxAAAgp8oLO96TySp2XRfBCQCAPDaiNCCfzS4l8hkH1mVHBCcAAPLYqLJC2a2oM3VgXXZEcAIAII8V+TyqKA3ILiedDEkVpQEV+ewZUey5KgAAkDPjy4tklzv/vYY0obz97QvsgOAEAECe61fs1/BeAcvDk9eQhpcG1Le47WaZdkFwAgAAmjKoRD6PtcnJ5zF0zsC2m2HaCcEJAACoyOfR1MElsmq/Sb9Hmjq4RIU2vbapmb1XBwAAcqaitECjywpzHp78Hml0WaEqSgty+8JdQHACAAAtJvYv1nG9C3IWnvweaWTvAk3sX5ybF+wm3nIFAAC0YpqmVtQ0am1dk2LJ7L1O85mmif2LZRg2ua2vEwQnAADQrqr6iCq3NiieNJXJt7PzGgcuBJ86uMQR9dzBCE4AAOCwwvGknqtu0Ka9USVMdWuXcUNfbjkwZWCJbTe57AjBCQAAdGpHY0yrasOqqo/KkBRPIz34jAOBq6I0oAnlRbbep6kzBCcAAJCycDypdXVN2lgfVW1TQvGkKZ9hyJQpUwfOKhkyFDdN+TyGygu9GlEa0KiyQkeeYToUwQkAAHRZQyyp2nBc0YSphGnKaxgKeA2VF/lUYtWmUFlEcAIAAEiR+6IgAABAlhCcAAAAUkRwAgAASBHBCQAAIEUEJwAAgBQRnAAAAFJEcAIAAEgRwQkAACBFBCcAAIAUEZwAAABSRHACAABIEcEJAAAgRQQnAACAFBGcAAAAUkRwAgAASBHBCQAAIEUEJwAAgBQRnAAAAFJEcAIAAEgRwQkAACBFBCcAAIAUEZwAAABSRHACAABI0f8HZTtvBcyEi0YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def mb_trinomial_tree_underlying_prices(n, S, K, T, r, v):\n",
    "    # Calculating delta T\n",
    "    dt = T/n\n",
    "\n",
    "    # Parameters for trinomial tree\n",
    "    dx = v * math.sqrt(3 * dt)\n",
    "    nu = r - 0.5 * v**2\n",
    "\n",
    "    # Initialize arrays for storing stock prices\n",
    "    stock_price = np.zeros((2*n+1, n+1))\n",
    "\n",
    "    # Calculate stock prices\n",
    "    for i in range(n+1):\n",
    "        for j in range(-i, i+1):\n",
    "            stock_price[j + n, i] = S * np.exp(j * dx)\n",
    "\n",
    "    # Create a graph object to represent the trinomial tree\n",
    "    trinomial_tree = nx.Graph()\n",
    "\n",
    "    # Add nodes to the tree with underlying prices\n",
    "    for i in range(n + 1):\n",
    "        for j in range(-i, i + 1):\n",
    "            trinomial_tree.add_node((i, j), pos=(i, n - j), value=stock_price[j + n, i])\n",
    "\n",
    "    # Add edges to the tree\n",
    "    for i in range(n):\n",
    "        for j in range(-i, i + 1):\n",
    "            if (i + 1, j + 1) in trinomial_tree.nodes:\n",
    "                trinomial_tree.add_edge((i, j), (i + 1, j + 1))\n",
    "            if (i + 1, j) in trinomial_tree.nodes:\n",
    "                trinomial_tree.add_edge((i, j), (i + 1, j))\n",
    "            if (i + 1, j - 1) in trinomial_tree.nodes:\n",
    "                trinomial_tree.add_edge((i, j), (i + 1, j - 1))\n",
    "\n",
    "    # Get node positions and underlying prices for plotting\n",
    "    pos = nx.get_node_attributes(trinomial_tree, 'pos')\n",
    "    labels = nx.get_node_attributes(trinomial_tree, 'value')\n",
    "\n",
    "    # Filter out nodes with no underlying price\n",
    "    labels = {key: f'{value:.2f}' for key, value in labels.items() if value is not None}\n",
    "\n",
    "    # Draw the trinomial tree\n",
    "    plt.figure(figsize=(8, 6))\n",
    "    nx.draw(trinomial_tree, pos, labels=labels, with_labels=True, node_color=\"skyblue\", node_size=1500)\n",
    "    plt.gca().invert_yaxis()  # Invert y-axis to align the first node at the top\n",
    "    plt.axis('off')  # Turn off axis display\n",
    "    plt.show()\n",
    "\n",
    "mb_trinomial_tree_underlying_prices(2, 100, 105, 1, 0.05, 0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f47ddb63-d740-4265-8cc9-2779146e9d19",
   "metadata": {},
   "source": [
    "#### Visualizing the call prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "edd44428-74c2-4002-9fef-93cd08af1597",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def mb_trinomial_tree_european_call(n, S, K, T, r, v):\n",
    "    # Calculating delta T\n",
    "    dt = T/n\n",
    "\n",
    "    # Parameters for trinomial tree\n",
    "    dx = v * math.sqrt(3 * dt)\n",
    "    nu = r - 0.5 * v**2\n",
    "    pu = 0.5 * ((v**2 * dt + nu**2 * dt**2) / dx**2 + nu * dt / dx)\n",
    "    pd = 0.5 * ((v**2 * dt + nu**2 * dt**2) / dx**2 - nu * dt / dx)\n",
    "    pm = 1 - pu - pd\n",
    "\n",
    "    # Initialize arrays for storing stock prices and option values\n",
    "    stock_price = np.zeros((2*n+1, n+1))\n",
    "    option_value = np.zeros((2*n+1, n+1))\n",
    "\n",
    "    # Calculate stock prices\n",
    "    for i in range(n+1):\n",
    "        for j in range(-i, i+1):\n",
    "            stock_price[j + n, i] = S * np.exp(j * dx)\n",
    "\n",
    "    # Calculate option values at maturity\n",
    "    option_value[:, n] = np.maximum(stock_price[:, n] - K, 0)\n",
    "\n",
    "    # Perform backward iteration to find option value at t=0\n",
    "    for j in range(n-1, -1, -1):\n",
    "        for i in range(-j, j+1):\n",
    "            option_value[i + n, j] = math.exp(-r * dt) * (\n",
    "                pu * option_value[i + n + 1, j + 1] + \n",
    "                pm * option_value[i + n, j + 1] + \n",
    "                pd * option_value[i + n - 1, j + 1]\n",
    "            )\n",
    "\n",
    "    # Create a graph object to represent the trinomial tree\n",
    "    trinomial_tree = nx.Graph()\n",
    "\n",
    "    # Add nodes to the tree with underlying prices and option values\n",
    "    for i in range(n + 1):\n",
    "        for j in range(-i, i + 1):\n",
    "            trinomial_tree.add_node((i, j), pos=(i, n - j), value=option_value[j + n, i])\n",
    "\n",
    "    # Add edges to the tree\n",
    "    for i in range(n):\n",
    "        for j in range(-i, i + 1):\n",
    "            if (i + 1, j + 1) in trinomial_tree.nodes:\n",
    "                trinomial_tree.add_edge((i, j), (i + 1, j + 1))\n",
    "            if (i + 1, j) in trinomial_tree.nodes:\n",
    "                trinomial_tree.add_edge((i, j), (i + 1, j))\n",
    "            if (i + 1, j - 1) in trinomial_tree.nodes:\n",
    "                trinomial_tree.add_edge((i, j), (i + 1, j - 1))\n",
    "\n",
    "    # Get node positions and option values for plotting\n",
    "    pos = nx.get_node_attributes(trinomial_tree, 'pos')\n",
    "    labels = nx.get_node_attributes(trinomial_tree, 'value')\n",
    "\n",
    "    # Filter out nodes with no option value\n",
    "    labels = {key: f'{value:.2f}' for key, value in labels.items() if value is not None}\n",
    "\n",
    "    # Draw the trinomial tree\n",
    "    plt.figure(figsize=(8, 6))\n",
    "    nx.draw(trinomial_tree, pos, labels=labels, with_labels=True, node_color=\"skyblue\", node_size=1500)\n",
    "    plt.gca().invert_yaxis()  # Invert y-axis to align the first node at the top\n",
    "    plt.axis('off')  # Turn off axis display\n",
    "    plt.show()\n",
    "\n",
    "mb_trinomial_tree_european_call(2, 100, 105, 1, 0.05, 0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c4657e8-d9de-442c-87a9-783c3c64db6b",
   "metadata": {},
   "source": [
    "#### Visualizing the put prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "17b5cb9f-2822-4d9d-91ec-8c59cb336f8c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def mb_trinomial_tree_european_put(n, S, K, T, r, v):\n",
    "    # Calculating delta T\n",
    "    dt = T/n\n",
    "\n",
    "    # Parameters for trinomial tree\n",
    "    dx = v * math.sqrt(3 * dt)\n",
    "    nu = r - 0.5 * v**2\n",
    "    pu = 0.5 * ((v**2 * dt + nu**2 * dt**2) / dx**2 + nu * dt / dx)\n",
    "    pd = 0.5 * ((v**2 * dt + nu**2 * dt**2) / dx**2 - nu * dt / dx)\n",
    "    pm = 1 - pu - pd\n",
    "\n",
    "    # Initialize arrays for storing stock prices and option values\n",
    "    stock_price = np.zeros((2*n+1, n+1))\n",
    "    option_value = np.zeros((2*n+1, n+1))\n",
    "\n",
    "    # Calculate stock prices\n",
    "    for i in range(n+1):\n",
    "        for j in range(-i, i+1):\n",
    "            stock_price[j + n, i] = S * np.exp(j * dx)\n",
    "\n",
    "    # Calculate option values at maturity\n",
    "    option_value[:, n] = np.maximum(K - stock_price[:, n], 0)\n",
    "\n",
    "    # Perform backward iteration to find option value at t=0\n",
    "    for j in range(n-1, -1, -1):\n",
    "        for i in range(-j, j+1):\n",
    "            option_value[i + n, j] = math.exp(-r * dt) * (\n",
    "                pu * option_value[i + n + 1, j + 1] + \n",
    "                pm * option_value[i + n, j + 1] + \n",
    "                pd * option_value[i + n - 1, j + 1]\n",
    "            )\n",
    "\n",
    "    # Create a graph object to represent the trinomial tree\n",
    "    trinomial_tree = nx.Graph()\n",
    "\n",
    "    # Add nodes to the tree with underlying prices and option values\n",
    "    for i in range(n + 1):\n",
    "        for j in range(-i, i + 1):\n",
    "            trinomial_tree.add_node((i, j), pos=(i, n - j), value=option_value[j + n, i])\n",
    "\n",
    "    # Add edges to the tree\n",
    "    for i in range(n):\n",
    "        for j in range(-i, i + 1):\n",
    "            if (i + 1, j + 1) in trinomial_tree.nodes:\n",
    "                trinomial_tree.add_edge((i, j), (i + 1, j + 1))\n",
    "            if (i + 1, j) in trinomial_tree.nodes:\n",
    "                trinomial_tree.add_edge((i, j), (i + 1, j))\n",
    "            if (i + 1, j - 1) in trinomial_tree.nodes:\n",
    "                trinomial_tree.add_edge((i, j), (i + 1, j - 1))\n",
    "\n",
    "    # Get node positions and option values for plotting\n",
    "    pos = nx.get_node_attributes(trinomial_tree, 'pos')\n",
    "    labels = nx.get_node_attributes(trinomial_tree, 'value')\n",
    "\n",
    "    # Filter out nodes with no option value\n",
    "    labels = {key: f'{value:.2f}' for key, value in labels.items() if value is not None}\n",
    "\n",
    "    # Draw the trinomial tree\n",
    "    plt.figure(figsize=(8, 6))\n",
    "    nx.draw(trinomial_tree, pos, labels=labels, with_labels=True, node_color=\"skyblue\", node_size=1500)\n",
    "    plt.gca().invert_yaxis()  # Invert y-axis to align the first node at the top\n",
    "    plt.axis('off')  # Turn off axis display\n",
    "    plt.show()\n",
    "\n",
    "mb_trinomial_tree_european_put(2, 100, 105, 1, 0.05, 0.2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c6bd9359-f13e-4896-9bb9-c2f1522014d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def mb_trinomial_tree_european_put(n, S, K, T, r, v):\n",
    "    # Calculating delta T\n",
    "    dt = T/n\n",
    "\n",
    "    # Parameters for trinomial tree\n",
    "    dx = v * math.sqrt(3 * dt)\n",
    "    nu = r - 0.5 * v**2\n",
    "    pu = 0.5 * ((v**2 * dt + nu**2 * dt**2) / dx**2 + nu * dt / dx)\n",
    "    pd = 0.5 * ((v**2 * dt + nu**2 * dt**2) / dx**2 - nu * dt / dx)\n",
    "    pm = 1 - pu - pd\n",
    "\n",
    "    # Initialize arrays for storing stock prices and option values\n",
    "    stock_price = np.zeros((2*n+1, n+1))\n",
    "    option_value = np.zeros((2*n+1, n+1))\n",
    "\n",
    "    # Calculate stock prices\n",
    "    for i in range(n+1):\n",
    "        for j in range(-i, i+1):\n",
    "            stock_price[j + n, i] = S * np.exp(j * dx)\n",
    "\n",
    "    # Calculate option values at maturity\n",
    "    option_value[:, n] = np.maximum(K - stock_price[:, n], 0)\n",
    "\n",
    "    # Perform backward iteration to find option value at t=0\n",
    "    for j in range(n-1, -1, -1):\n",
    "        for i in range(-j, j+1):\n",
    "            option_value[i + n, j] = math.exp(-r * dt) * (\n",
    "                pu * option_value[i + n + 1, j + 1] + \n",
    "                pm * option_value[i + n, j + 1] + \n",
    "                pd * option_value[i + n - 1, j + 1]\n",
    "            )\n",
    "\n",
    "    # Create a graph object to represent the trinomial tree\n",
    "    trinomial_tree = nx.Graph()\n",
    "\n",
    "    # Add nodes to the tree with underlying prices and option values\n",
    "    for i in range(n + 1):\n",
    "        for j in range(-i, i + 1):\n",
    "            trinomial_tree.add_node((i, j), pos=(i, n - j), value=option_value[j + n, i])\n",
    "\n",
    "    # Add edges to the tree\n",
    "    for i in range(n):\n",
    "        for j in range(-i, i + 1):\n",
    "            if (i + 1, j + 1) in trinomial_tree.nodes:\n",
    "                trinomial_tree.add_edge((i, j), (i + 1, j + 1))\n",
    "            if (i + 1, j) in trinomial_tree.nodes:\n",
    "                trinomial_tree.add_edge((i, j), (i + 1, j))\n",
    "            if (i + 1, j - 1) in trinomial_tree.nodes:\n",
    "                trinomial_tree.add_edge((i, j), (i + 1, j - 1))\n",
    "\n",
    "    # Get node positions and option values for plotting\n",
    "    pos = nx.get_node_attributes(trinomial_tree, 'pos')\n",
    "    labels = nx.get_node_attributes(trinomial_tree, 'value')\n",
    "\n",
    "    # Filter out nodes with no option value\n",
    "    labels = {key: f'{value:.2f}' for key, value in labels.items() if value is not None}\n",
    "\n",
    "    # Draw the trinomial tree\n",
    "    plt.figure(figsize=(8, 6))\n",
    "    nx.draw(trinomial_tree, pos, labels=labels, with_labels=True, node_color=\"skyblue\", node_size=1500)\n",
    "    plt.gca().invert_yaxis()  # Invert y-axis to align the first node at the top\n",
    "    plt.axis('off')  # Turn off axis display\n",
    "    plt.show()\n",
    "\n",
    "mb_trinomial_tree_european_put(10, 100, 105, 1, 0.05, 0.2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7203579-3977-4bf8-b455-dee6b8243e80",
   "metadata": {},
   "source": [
    "## Black and Scholes model mb_black_scholes function for comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "3b997f60-f685-4a1d-aa41-dcbef1bae4c8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Black-Scholes price of the call option is: 8.021352235143176\n",
      "The Black-Scholes price of the put option is: 7.9004418077181455\n"
     ]
    }
   ],
   "source": [
    "# mb_black_scholes function needs the following variables:\n",
    "# S: spot price\n",
    "# K: strike price\n",
    "# T: time to maturity\n",
    "# r: interest rate\n",
    "# v: volatility of underlying asset\n",
    "\n",
    "def mb_black_scholes(S, K, T, r, v, option = 'call'):\n",
    "    d1 = (np.log(S / K) + (r + 0.5 * v ** 2) * T) / (v * np.sqrt(T))\n",
    "    d2 = (np.log(S / K) + (r - 0.5 * v ** 2) * T) / (v * np.sqrt(T))\n",
    "    if option == 'call':\n",
    "        result = (S * si.norm.cdf(d1, 0.0, 1.0) - K * np.exp(-r * T) * si.norm.cdf(d2, 0.0, 1.0))\n",
    "    if option == 'put':\n",
    "        result = (K * np.exp(-r * T) * si.norm.cdf(-d2, 0.0, 1.0) - S * si.norm.cdf(-d1, 0.0, 1.0))\n",
    "    return result\n",
    "\n",
    "call_price = mb_black_scholes(100, 105, 1, 0.05, 0.2, option = 'call')\n",
    "put_price = mb_black_scholes(100, 105, 1, 0.05, 0.2, option = 'put')\n",
    "\n",
    "print(f\"The Black-Scholes price of the call option is: {call_price}\")\n",
    "print(f\"The Black-Scholes price of the put option is: {put_price}\")"
   ]
  }
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